Dirac gauginos and unification in F-theory

Supersymmetric models in which the gauginos acquire Dirac masses, rather than Majorana masses, offer an appealing alternative to the minimal supersymmetric standard model, especially in the light of the bounds set on superpartner masses by the 2011 LHC data. Dirac gauginos require the presence of chiral multiplets in the adjoint representation of the gauge group, and the realisation of such scenarios in F-theory is the subject of this paper. The chiral adjoints drastically alter the usual picture of gauge coupling unification, but this is disturbed anyway in F-theory models with non-trivial hypercharge flux. The interplay between these two factors is explored, and it is found for example that viable F-theory unification can be achieved at around the reduced Planck scale, if there is an extra vector-like pair of singlet leptons with TeV-scale mass. I then discuss the conditions which must be satisfied by the geometry and hypercharge flux of an F-theory model with Dirac gauginos. One nice possibility is for the visible sector to be localised on a K3 surface, and this is discussed in some detail. Finally, I describe how to achieve an unbroken discrete R-symmetry in such compactifications, which is an important ingredient in many models with Dirac gauginos, and write down a simple example which has adjoint chiral multiplets, an appropriate R-symmetry, and allows for viable breaking of SU(5) by hypercharge flux.